Approaches to Quantum Gravity

Questions and answers• Q - J. Henson - to J. Ambjørn et al.1. The CDT program borrows many techniques from lattice quantum field theory,and as there, some universality properties are presumably crucial here –many methods of discretisation should result in the same model in the continuumlimit. But in this new type of model we cannot yet have the same level ofconfidence in this principle. Apart from the very encouraging results that yousummarise above, which show that the model does have some desirable properties,what is known specifically about universality in this type of discretisedQuantum Gravity model?2. Although the cut-off is diffeomorphism invariant in the sense that the discretegeometries only contain lengths and topological information, they are notin another important sense: the discretisation picks out a preferred foliation ofspacetime, and one would expect that, were matter to be included, modes thatwere high frequency with respect to this foliation would be cut off. Then thehope would be, as in lattice QFT, that this discrete symmetry breaking has nosignificance in the continuum limit. What arguments are there for this, and canyou envision a calculation that would verify it?–A-J.Ambjørnet al.:1. Not much is known about universality except the simple test of changingthe coupling constants somewhat and observing the correlators can bemapped onto each other by rescaling of the time direction relative to the spacedirection.2. We simply do not know how the combined system of matter and geometrywill behave. One can only hope that the time-foliation does not spoil the generalproperties of the matter system one would expect in GR. In flat spacetimewe are of course allowed to consider an asymmetric lattice where the latticespacing in the time direction is different from the lattice spacing in the spatialdirections. It should not make any difference provided our action is adjustedcorrespondingly.414